Adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method for injection molding process

This paper presents an adaptive method that couples the finite element (FE) method and the meshfree (MF) method in the arbitrary Lagrangian–Eulerian (ALE) description for numerical simulation of injection molding processes. The ALE feature is used to accurately capture moving free surfaces of flow problems and, meanwhile, to alleviate mesh distortion and its influence on the accuracy and robustness of numerical solutions. Based on the continuous blending method, originally presented for properly imposing the essential boundary conditions in MF methods, the coupled ALE FE and MF method is developed, to exploit the respective advantages of both FE and MF methods, but to avoid their respective weak points. The method features self-adaptivity in view of the fact that moving free surfaces in an injection molding process are continuously advanced. The Pressure-stabilized Fractional Step Algorithm, in which the modified version of the finite increment calculus process is extended to the coupled ALE FE and MF method, is used to solve incompressible Navier–Stokes equations governing the injected polymer flow, so that equal low-order u− p interpolations that violate the LBB condition can be effectively used. Numerical experiments demonstrate the significance and ability of the proposed method for numerical simulation of injection molding processes. Copyright q 2007 John Wiley & Sons, Ltd